Heretofore, there has been utilized a secondary battery including a positive electrode band and a negative electrode band, both being overlapped and wound together. As such a secondary battery, there is a cylindrical battery including electrode bands wound in circular columnar form and contained in a cylindrical case. For example, some cylindrical batteries to be used in a vehicle (especially HV and EV) are designed in a slender form because of the necessity to be mounted therein. Conventional examples of the cylindrical battery are disclosed in Patent Literatures 1 and 2. In this type of cylindrical battery, an end of the cylindrical case is closed by a cover member whereby the inside of the cylindrical case is separated from the outside. At the center of the cover member, a terminal connected to one of the electrode bands is provided.